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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# from qiskit import IBMQ\n",
    "# TOKEN = '043e4ac348a7f7731a10fb4ec608e25dac8ddcffd66abbe43bb0bf3079242609ddfa9aa12b188c423f2f39f3e5b8fa384ef3de570b69f1606a9033fb44ad3410'\n",
    "# IBMQ.save_account(TOKEN, overwrite=True)\n",
    "# IBMQ.load_account()\n",
    "# IBMQ.providers()\n",
    "# provider = IBMQ.get_provider(group='open')\n",
    "# for i in provider.backends():\n",
    "#     print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import BasicAer, execute, QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.ignis.verification.tomography import count_keys\n",
    "from qiskit.aqua.components.optimizers import COBYLA\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # The Ising Model\n",
    "# n = 3\n",
    "# p = 2 * n\n",
    "# J = np.zeros((n, n))\n",
    "# J[0, 1] = 8\n",
    "# J[0, 2] = 6\n",
    "# J[1, 2] = 24\n",
    "\n",
    "# h = np.zeros(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = [5, 2, 1]\n",
    "c = [2, 5, 10]\n",
    "W_max = 2\n",
    "# 0 0 1 1 0\n",
    "\n",
    "w = [1, 5, 2]\n",
    "c = [10, 2, 5]\n",
    "W_max = 2\n",
    "# 1 0 0 0 1\n",
    "# 0 1 1 0 1\n",
    "# 0 0 1 0 1\n",
    "\n",
    "A = max(c)\n",
    "B = 0.5\n",
    "\n",
    "n = len(w) + W_max\n",
    "p = 2 * n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_function(W_max, w, c, A, B):\n",
    "    w = np.array(w)\n",
    "    c = np.array(c)\n",
    "    # Helper array [1, 2, ..., W_max]\n",
    "    N = np.arange(1, W_max + 1)\n",
    "    # Initialize the matrix of size W_max + m\n",
    "    out = np.zeros((W_max + len(w), W_max + len(w)))\n",
    "    # Adding the Ha part\n",
    "    out[:W_max, :W_max] += A * -2 * np.identity(W_max)\n",
    "    out[:W_max, :W_max] += A * np.ones((W_max, W_max)) \n",
    "    out[:W_max, :W_max] += A * N[:, np.newaxis] * N[np.newaxis, :]\n",
    "    out[W_max:, W_max:] += A * w[:, np.newaxis] * w[np.newaxis, :]\n",
    "    out[:W_max, W_max:] += A * -N[:, np.newaxis] * w[np.newaxis, :]\n",
    "    out[W_max:, :W_max] += A * -w[:, np.newaxis] * N[np.newaxis, :]\n",
    "    # Adding the Hb part\n",
    "    out[W_max:, W_max:] += -B * np.diag(c)\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = cost_function(W_max, w, c, A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "J = np.triu(Q, k=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# J = Q.copy()\n",
    "# np.fill_diagonal(J, 0)\n",
    "h = np.diag(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[   0.,   30.,  -10.,  -50.,  -20.],\n       [   0.,    0.,  -20., -100.,  -40.],\n       [   0.,    0.,    0.,   50.,   20.],\n       [   0.,    0.,    0.,    0.,  100.],\n       [   0.,    0.,    0.,    0.,    0.]])"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([  0. ,  30. ,   5. , 249. ,  37.5])"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "betas = np.pi * np.random.rand(p)\n",
    "gammas = np.pi * np.random.rand(p)\n",
    "\n",
    "params = list()\n",
    "for i in range(p):\n",
    "    params.append(gammas[i])\n",
    "    params.append(betas[i])\n",
    "params = np.array(params)\n",
    "initial_params = params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def qaoa_circuit(params):\n",
    "    q = QuantumRegister(n)\n",
    "    c = ClassicalRegister(n)\n",
    "    circ = QuantumCircuit(q, c)\n",
    "    \n",
    "    # Initializing the circuit by Hadamard-Gates\n",
    "    for i in range(n):\n",
    "        circ.h(q[i])\n",
    "    circ.barrier()\n",
    "\n",
    "    for k in range(p):\n",
    "        gamma = params[2 * k]\n",
    "        beta = params[2 * k + 1]\n",
    "\n",
    "        for i in range(J.shape[0]):\n",
    "            for j in range(J.shape[1]):\n",
    "                if J[i,j] != 0:\n",
    "                    circ.cx(i, j)\n",
    "                    circ.rz(-2 * gamma * J[i,j], j)\n",
    "                    circ.cx(i, j)\n",
    "            circ.barrier()\n",
    "\n",
    "        for i in range(len(h)):\n",
    "            if h[i] != 0:\n",
    "                circ.rz(-2 * gamma * h[i], i)\n",
    "        circ.barrier()\n",
    "\n",
    "        for j in range(n):\n",
    "            circ.rx(2 * beta, j)\n",
    "        circ.barrier()\n",
    "\n",
    "    circ.measure(q, c)\n",
    "\n",
    "    return circ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "circ = qaoa_circuit(params)\n",
    "# circ.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cut_counts(counts, bit_indexes):\n",
    "    bit_indexes.sort(reverse=True)\n",
    "    new_counts = {}\n",
    "    for key in counts:\n",
    "        new_key = ''\n",
    "        for index in bit_indexes:\n",
    "            new_key += key[-1 - index]\n",
    "        if new_key in new_counts:\n",
    "            new_counts[new_key] += counts[key]\n",
    "        else:\n",
    "            new_counts[new_key] = counts[key]\n",
    "\n",
    "    return new_counts\n",
    "\n",
    "def get_all_counts(counts: dict, number_of_qubits):\n",
    "    all_counts = dict()\n",
    "    keys = count_keys(number_of_qubits)\n",
    "    for key in keys:\n",
    "        if key in counts:\n",
    "            all_counts[key] = counts[key]\n",
    "        else:\n",
    "            all_counts[key] = 0\n",
    "    return all_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def circuit_results(circuit):\n",
    "    # A simulator is used here instead of real hardware\n",
    "    backend = BasicAer.get_backend('qasm_simulator')\n",
    "    shots = 30000\n",
    "    result = execute(circuit, backend=backend, shots=shots).result()\n",
    "    \n",
    "    # backend = provider.get_backend('ibmq_london')\n",
    "    # result = execute(circ, backend).result()\n",
    "\n",
    "    # Getting and return results as a dictionary and as an output_distribution with all values between 0 and 1.\n",
    "    counts = result.get_counts(circuit)\n",
    "    all_counts = get_all_counts(counts, circuit.num_qubits)\n",
    "    output_distribution = [v / shots for v in all_counts.values()]\n",
    "    return all_counts, output_distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
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\n"
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "source": [
    "before_optimizing = circuit_results(circ)[0]\n",
    "plot_histogram(before_optimizing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0.0 1.0\n"
    }
   ],
   "source": [
    "def ising_to_qubo(s):\n",
    "    return 0.5 + 0.5 * s\n",
    "print(qubo_to_ising(-1),\n",
    "      qubo_to_ising(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A(1 - sum(0.5 + 0.5 * y))^2 + A(sum(n*(0.5+0.5*y)) - sum(w * (0.5+0.5*x)))^2 - B*sum(c*(0.5+0.5*x))\n",
    "A(n - sum(y))^2 + A(sum(n*(0.5+0.5*y)) - sum(w * (0.5+0.5*x)))^2 - B*sum(c*(0.5+0.5*x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "Z = np.array([[1, 0], [0, -1]])\n",
    "I = np.eye(2)\n",
    "# Z2 = (I - Z) / 2\n",
    "\n",
    "C = np.zeros((2**n, 2**n))\n",
    "for i in range(n):\n",
    "    for j in range(n):\n",
    "        res = J[i, j]\n",
    "        for k in range(n):\n",
    "            if i == k or j == k:\n",
    "                res = np.kron(res, Z)\n",
    "            else:\n",
    "                res = np.kron(res, I)\n",
    "        C += res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ -40.,    0.,    0., ...,    0.,    0.,    0.],\n       [   0., -160.,    0., ...,    0.,    0.,    0.],\n       [   0.,    0.,  -40., ...,    0.,    0.,    0.],\n       ...,\n       [   0.,    0.,    0., ...,  -40.,    0.,    0.],\n       [   0.,    0.,    0., ...,    0., -160.,    0.],\n       [   0.,    0.,    0., ...,    0.,    0.,  -40.]])"
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "source": [
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective_function(params):\n",
    "    # constructing the circuit, in this example, make sure circ already exists\n",
    "    circ = qaoa_circuit(params)\n",
    "    \n",
    "    # retrieve the results of the quantum circuit\n",
    "    _, output_distribution = circuit_results(circ)\n",
    "    \n",
    "    # calculate the cost function by using the equation above\n",
    "    cost = np.transpose(output_distribution) @ C @ output_distribution\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "(array([3.4802259 , 1.63149564, 0.84822659, 3.01911337, 1.36445833,\n       1.39310949, 1.77352875, 0.58123774, 2.14176284, 0.82892184,\n       1.85362548, 1.97798312, 0.74039384, 1.21832477, 1.58815706,\n       1.59961383, 2.63553846, 2.37891172, 2.84133493, 1.22103103]), -23.093530222222224, 155)\n"
    }
   ],
   "source": [
    "# A COBYLA instance with 500 iterations max and a tolerance level of 0.001\n",
    "optimizer = COBYLA(maxiter=500, tol=0.001)\n",
    "\n",
    "# Performing the optimization\n",
    "ret = optimizer.optimize(num_vars=len(params), objective_function=objective_function, initial_point=params)\n",
    "\n",
    "# Printing the results\n",
    "print(ret)\n",
    "\n",
    "# Using the new parameters and constructing the new parameterized circuit\n",
    "new_params = ret[0]\n",
    "circ_after = qaoa_circuit(new_params)\n",
    "\n",
    "# Getting the results of the optimized circuit\n",
    "after_optimizing = circuit_results(circ_after)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
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\n"
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "source": [
    "plot_histogram(after_optimizing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "{'00000': 1019, '00001': 63, '00010': 678, '00011': 817, '00100': 1954, '00101': 2143, '00110': 85, '00111': 12, '01000': 54, '01001': 1756, '01010': 10442, '01011': 1, '01100': 232, '01101': 407, '01110': 898, '01111': 404, '10000': 217, '10001': 32, '10010': 167, '10011': 3287, '10100': 83, '10101': 301, '10110': 2282, '10111': 84, '11000': 288, '11001': 66, '11010': 60, '11011': 581, '11100': 295, '11101': 1086, '11110': 90, '11111': 116}\n"
    }
   ],
   "source": [
    "print(after_optimizing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}